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# Brushless Hall sensor frequency calculator

The following formcalculates the angular velocity of a motor based on the Hall effect sensor signal and vice versa. See below for more details about the online calculator.

## Signals

The folloging figure illustrates the signal of the Hall effect sensors (H1, H2 and H3). The combination of the three sensors is also illustrated. This last one (F2 or T2) allows high rate angular velocity measurement since it is three times faster than a single Hall effect sensor.

## Formulas

Let's consider the simplest configuration: 3 sensors, 2 poles and an angular velocity of 1 revolutions per second (60 rpm). When the rotor performs one revolution, the north pole and the south pole are in front of the sensor just one time. During one revolution, the sensor output will be half of the time at high level, and half the time at low level. In this configuration, one revolution is equal to one period. The first formula describes how the frequency F1 (or period T1) can be calculated:

$$F1_{Hz} = \frac { N_{rps} \times N_{poles} } {2}$$

The following describes how the frequency F2 (or period T2) can be calculated:

$$F2_{Hz} = 4 \times N_{hall} \times F1 = 2 \times N_{rps} \times N_{poles} \times N_{hall}$$

Where:

• $$N_{poles}$$ is the number of poles (not the number of pair of poles)
• $$N_{rps}$$ is the angular velocity in revolution per second
• $$N_{hall}$$ is the number of hall sensor (typically 3)